Sharp null-energy lower bounds for Page-like entropy excursions in two-dimensional conformal field theory
Abstract
We derive sharp lower bounds on the energy cost of Page-like entanglement entropy excursions in two-dimensional conformal field theory. For states satisfying the primary quantum null energy condition (QNEC), the positive null energy E+ obeys a sharp lower bound with two branches separated by the threshold ΔS=(c/6)ln 2. We also derive a sharp lower bound on the net energy Enet, with a coefficient larger by a factor of two than the value quoted by Abdolrahimi and Page [Phys. Rev. D 92, 083005 (2015)] and, in the QNEC-saturating sector, we obtain a sharp lower bound on the negative energy E-. The constants are sharp as infima over smooth conformal vacua. We determine the entropy profiles that minimize E+ for general QNEC states and the one that minimizes E- in the saturating sector. Finally, for an excursion containing an infinite sequence of small sub-excursions within a finite duration, we derive a necessary condition for the total positive energy to remain finite, which is stronger than requiring the entropy to have finite total variation.
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BibTeX
@misc{karmoudi2026sharp,
title = {{Sharp null-energy lower bounds for Page-like entropy excursions in two-dimensional conformal field theory}},
author = {Soufiane Karmoudi and Mohammed Daoud},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.03576},
eprint = {2610.03576},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.03576},
}
RIS
TY - UNPB
TI - Sharp null-energy lower bounds for Page-like entropy excursions in two-dimensional conformal field theory
AU - Soufiane Karmoudi
AU - Mohammed Daoud
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2610.03576
UR - https://arxiv.org/abs/2610.03576
AB - We derive sharp lower bounds on the energy cost of Page-like entanglement entropy excursions in two-dimensional conformal field theory. For states satisfying the primary quantum null energy condition (QNEC), the positive null energy E_+ obeys a sharp lower bound with two branches separated by the threshold ΔS=(c/6)ln 2. We also derive a sharp lower bound on the net energy E_net, with a coefficient larger by a factor of two than the value quoted by Abdolrahimi and Page [Phys. Rev. D 92, 083005 (2015)] and, in the QNEC-saturating sector, we obtain a sharp lower bound on the negative energy E_-. The constants are sharp as infima over smooth conformal vacua. We determine the entropy profiles that minimize E_+ for general QNEC states and the one that minimizes E_- in the saturating sector. Finally, for an excursion containing an infinite sequence of small sub-excursions within a finite duration, we derive a necessary condition for the total positive energy to remain finite, which is stronger than requiring the entropy to have finite total variation.
ER -